Nicht aus der Schweiz? Besuchen Sie lehmanns.de
Invariance Theory - Peter B. Gilkey

Invariance Theory

The Heat Equation and the Atiyah-Singer Index Theorem

(Autor)

Buch | Hardcover
530 Seiten
1994
Crc Press Inc (Verlag)
978-0-8493-7874-4 (ISBN)
CHF 449,95 inkl. MwSt
This book treats the Atiyah-Singer index theorem using the heat equation, which gives a local formula for the index of any elliptic complex. Heat equation methods are also used to discuss Lefschetz fixed point formulas, the Gauss-Bonnet theorem for a manifold with smooth boundary, and the geometrical theorem for a manifold with smooth boundary. The author uses invariance theory to identify the integrand of the index theorem for classical elliptic complexes with the invariants of the heat equation.

Gilkey, Peter B.

Pseudo-Differential Operators Introduction Fourier Transform and Sobolev Spaces Pseudo-Differential Operators on Rm Pseudo-Differential Operators on Manifolds Index of Fredholm Operators Elliptic Complexes Spectral Theory The Heat Equation Local Index Formula Variational Formulas Lefschetz Fixed Point Theorems The Zeta Function The Eta Function Characteristic Classes Introduction Characteristic Classes of Complex Bundles Characteristic Classes of Real Bundles Complex Projective Space Invariance Theory The Gauss-Bonnet Theorem Invariance Theory and Pontrjagin Classes Gauss-Bonnet for Manifolds with Boundary Boundary Characteristic Classes Singer's Question The Index Theorem Introduction Clifford Modules Hirzebruch Signature Formula Spinors The Spin Complex The Riemann-Roch Theorem K-Theory The Atiyah-Singer Index Theorem The Regularity at s = 0 of the Eta Function Lefschetz Fixed Point Formulas Index Theorem for Manifolds with Boundary The Eta Invariant of Locally Flat Bundles Spectral Geometry Introduction Operators of Laplace Type Isospectral Manifolds Non-Minimal Operators Operators of Dirac Type Manifolds with Boundary Other Asymptotic Formulas The Eta Invariant of Spherical Space Forms A Guide to the Literature Acknowledgment Introduction Bibliography Notation

Erscheint lt. Verlag 22.12.1994
Reihe/Serie Studies in Advanced Mathematics
Verlagsort Bosa Roca
Sprache englisch
Maße 156 x 234 mm
Gewicht 1110 g
Einbandart gebunden
Themenwelt Mathematik / Informatik Mathematik Angewandte Mathematik
Naturwissenschaften Physik / Astronomie
ISBN-10 0-8493-7874-5 / 0849378745
ISBN-13 978-0-8493-7874-4 / 9780849378744
Zustand Neuware
Haben Sie eine Frage zum Produkt?
Mehr entdecken
aus dem Bereich
Anwendungen und Theorie von Funktionen, Distributionen und Tensoren

von Michael Karbach

Buch | Softcover (2023)
De Gruyter Oldenbourg (Verlag)
CHF 97,90